values government purchases is governed by the parameter 6. Suppose Robinson Crusoe's budget constraint is C = wH T, where w denotes the wage rate and T denotes lump sum taxes paid by Robinson Crusoe. Assume for simplicity that the government runs a balanced budget, i.e., that G = T. Notice, also, that the resource constraint in this economy implies that Y = C + G, i.e., consumption plus government purchases cannot exceed the amount of output produced Y. In this model, we will treat C, H, and Y as endogenous variables. All other variables including G and T are considered exogenous. a) (10 points) Derive Robinson Crusoe's labor supply curve. (Hint: Since G is exogenous, Robinson Crusoe treats it as a constant.) b) [20 points) Suppose the production function in the economy is Y = AH and the wage is thus given by w = A as in Problem Set 1. Use this equation, Robinson Crusoe's labor supply curve, the economy's resource constraint andfor the balanced budget equation to solve for output in terms ofonly G, A, and 1;). c) (10 points} The government purchases multiplier is dened as the number of dollars that output rises by when government purchases rise by one dollar. (You can assume for simplicity that all the endogenous variables are denoted in dollars.) What is the government purchases multiplier in this economy? [tip :> 0, what is the range of values that the government purchases multiplier can take? d) (10 points} Solve for consumption in terms of only G, A, and 11:. Briey comment on how an increase in government purchases affects consumption. e) (10 points} In one paragraph, discuss whether an increase in government purchases makes Robinson Crusoe better or worse o. In particular, comment on whether Robinson Crusoe is made better o in the case where he does not value the things the government purchases, i.e., if 3 = 0